Solve for n in $4^{n} + 4^{n} + 4^{n} + 4^{n} = 2^{2010}$

1005

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2010

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1004

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1003

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Solution

The correct option is C 1004
Given, $4^{n} + 4^{n} + 4^{n} + 4^{n} = 2^{2010}$
$\Rightarrow 4 \times 4^{n} = 2^{2010}$
$\Rightarrow 2^{2 n} = 2^{2008}$
On equating, we get
$2 n = 2008$
$\Rightarrow n = 1004$
Therefore, Option C is correct.

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